Here, we are looking at growth rates for two species of commercial mushrooms: Pleurotus ostreotus and P. cornucopiae.
Let’s take a quick look at the data structure:
| Species | Light | Nitrogen | Humidity | Temperature | GrowthRate |
|---|---|---|---|---|---|
| P.ostreotus | 0 | 0 | Low | 20 | 23.924 |
| P.ostreotus | 10 | 0 | Low | 20 | 34.132 |
| P.ostreotus | 20 | 0 | Low | 20 | 134.782 |
| P.ostreotus | 0 | 5 | Low | 20 | 44.516 |
| P.ostreotus | 10 | 5 | Low | 20 | 44.252 |
We have a few variables that were measured, and the outcome of growth rate is in g/day. The independent variables were…
## [1] "Species" "Light" "Nitrogen" "Humidity" "Temperature"
## [6] "GrowthRate"
Okay, let’s take a look at this data graphically:
The purpose of this data set was to find the combination of inputs that led the fastest mushroom growth for sale at the farmers’ market.
Let’s look at that.
Here are the conditions where the max growth rate was found:
| Species | Light | Nitrogen | Humidity | Temperature | GrowthRate |
|---|---|---|---|---|---|
| P.cornucopiae | 20 | 20 | High | 20 | 664.6693 |
## [1] 664.6693
Here’s a simple model and a list of significant predictors:
## GrowthRate ~ Light + Species + Nitrogen + Humidity + Temperature
##
## Call:
## glm(formula = GrowthRate ~ Light + Species + Nitrogen + Humidity +
## Temperature, data = df)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -112.19 -47.32 -8.48 35.45 418.31
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 216.0488 46.4242 4.654 5.77e-06 ***
## Light 5.5128 0.6063 9.093 < 2e-16 ***
## SpeciesP.ostreotus -48.3807 9.9005 -4.887 2.03e-06 ***
## Nitrogen -0.1579 0.3321 -0.476 0.6349
## HumidityLow -86.5783 9.9005 -8.745 7.26e-16 ***
## Temperature -3.8394 1.9801 -1.939 0.0538 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 5293.069)
##
## Null deviance: 2101436 on 215 degrees of freedom
## Residual deviance: 1111544 on 210 degrees of freedom
## AIC: 2472.9
##
## Number of Fisher Scoring iterations: 2
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 216.048767 | 46.424241 | 4.653792 | 5.8e-06 |
| Light | 5.512764 | 0.606279 | 9.092785 | 0.0e+00 |
| SpeciesP.ostreotus | -48.380660 | 9.900495 | -4.886691 | 2.0e-06 |
| HumidityLow | -86.578337 | 9.900495 | -8.744850 | 0.0e+00 |
## Start: AIC=2472.91
## GrowthRate ~ Light + Species + Nitrogen + Humidity + Temperature
##
## Df Deviance AIC
## - Nitrogen 1 1112741 2471.2
## <none> 1111544 2472.9
## - Temperature 1 1131445 2474.8
## - Species 1 1237942 2494.2
## - Humidity 1 1516318 2538.0
## - Light 1 1549169 2542.6
##
## Step: AIC=2471.15
## GrowthRate ~ Light + Species + Humidity + Temperature
##
## Df Deviance AIC
## <none> 1112741 2471.2
## - Temperature 1 1132641 2473.0
## - Species 1 1239138 2492.4
## - Humidity 1 1517515 2536.2
## - Light 1 1550365 2540.8
## GrowthRate ~ Light + Species + Humidity + Temperature
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 212.364338 | 45.6890416 | 4.648037 | 0.0000059 |
| Light | 5.512764 | 0.6051661 | 9.109505 | 0.0000000 |
| SpeciesP.ostreotus | -48.380660 | 9.8823217 | -4.895678 | 0.0000019 |
| HumidityLow | -86.578337 | 9.8823217 | -8.760931 | 0.0000000 |
| Temperature | -3.839376 | 1.9764643 | -1.942547 | 0.0534016 |
And now, since it’s a final project, Dr. Zahn wants many pretty pictures: